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Interpolation of Compact-Operators: The Multidimensional Case

Cobos, Fernando and Peetre, Jaak (1991) Interpolation of Compact-Operators: The Multidimensional Case. Proceedings of the London Mathematical Society , 63 (2). pp. 371-400. ISSN 0024-6115

Official URL: http://plms.oxfordjournals.org/content/s3-63/2/371.short

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Abstract

We investigate how compact operators behave under J and K interpolation methods for N spaces and two parameters. First we study those methods: relationship with those already existing in the literature, estimates for the norms of interpolated operators, examples, characterization as Aronszajn-Gagliardo functors,.... We also describe the relationship between Sparr and Fernandez methods and we derive sharp estimates for the norms of interpolated operators in Fernandez' case. Then we investigate the behaviour of compact operators. We begin with the case when one of the N-tuples reduces to a single Banach space, and later we treat the general case by means of the approach developed in [8].

Item Type:Article
Uncontrolled Keywords:Banach-Spaces; Real
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15511
Deposited On:07 Jun 2012 08:30
Last Modified:22 Oct 2013 16:26

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